Possibilistic Stable Models

Abstract

We present the main lines of a new framework that we have defined in order to improve the knowledge representation power of Answer Set Programming paradigm.
Our proposal is to use notions from possibility theory to extend the stable model semantics by taking into account a certainty level, expressed in terms of necessity measure, on each rule of a normal logic program.
First of all, we introduce possibilistic definite logic programs and show how to compute the conclusions of such programs both in syntactic and semantic ways. The syntactic handling is done by help of a fix-point operator, the semantic part relies on a possibility distribution on all sets of atoms and the two approaches are shown to be equivalent.
In a second part, we define what is a possibilistic stable model for a normal logic program, with default negation. Again, we define a possibility distribution allowing to determine the stable models.
We end our presentation by showing how we can use our framework to adressing inconsistency in Answer Set Programming.